11th Grade Limits and Continuity Quizzes

These quizzes are designed for Grade 11 students, typically in a Pre-Calculus course. The content serves as a formal introduction to the concepts of limits and continuity, preparing students for a subsequent course in AP Calculus or college-level calculus.

Introduce continuity with the informal idea of drawing a graph without lifting your pencil. Then, formalize this with the three-part definition: f(c) is defined, the limit as x approaches c exists, and the limit equals the function's value. Use graphical examples of removable, jump, and infinite discontinuities to illustrate what happens when each condition fails.

Students will practice a range of foundational limit skills, including evaluating one-sided and two-sided limits from graphs and equations. The problems also require students to apply the definition of continuity to determine if a function is continuous at a specific point and to identify the type and location of any discontinuities.

Students often correctly identify that a function has a 'break' but struggle to use precise mathematical language to describe why it's discontinuous. They might say a function with a hole is not continuous but fail to specify that it's because the function is undefined at that point, violating the first part of the continuity test.

These quizzes are available as both printable PDFs and interactive digital activities. You can use the digital version in class for immediate feedback and collaborative practice, then assign the printable PDF for homework to encourage offline, focused problem-solving. Each format comes with a complete answer key for easy review.

The study of limits in Grade 11 directly builds upon students' prior analysis of functions, particularly rational functions. Concepts like identifying vertical asymptotes and holes in rational functions are re-framed using the more precise language of infinite limits and removable discontinuities, setting the stage for calculus.